GeographicLib: GeographicLib::GeodesicLineExact Class Reference (original) (raw)

An exact geodesic line. More...

#include <[GeographicLib/GeodesicLineExact.hpp](GeodesicLineExact%5F8hpp%5Fsource.html)>

An exact geodesic line.

GeodesicLineExact facilitates the determination of a series of points on a single geodesic. This is a companion to the GeodesicExact class. For additional information on this class see the documentation on the GeodesicLine class.

Example of use:

#include

#include

#include

#include

using namespace std;

try {

GeodesicExact geod(Constants::WGS84_a(), Constants::WGS84_f());

double

lat1 = 40.640, lon1 = -73.779,

lat2 = 1.359, lon2 = 103.989;

double ds0 = 500e3;

int num = int(ceil(line.Distance() / ds0));

cout << fixed << setprecision(3);

{

double ds = line.Distance() / num;

for (int i = 0; i <= num; ++i) {

double lat, lon;

line.Position(i * ds, lat, lon);

cout << i << " " << lat << " " << lon << "\n";

}

}

{

double da = line.Arc() / num;

for (int i = 0; i <= num; ++i) {

double lat, lon;

line.ArcPosition(i * da, lat, lon);

cout << i << " " << lat << " " << lon << "\n";

}

}

}

catch (const exception& e) {

cerr << "Caught exception: " << e.what() << "\n";

return 1;

}

}

int main(int argc, const char *const argv[])

Header for GeographicLib::Constants class.

Header for GeographicLib::GeodesicExact class.

Header for GeographicLib::GeodesicLineExact class.

Exact geodesic calculations.

Math::real Position(real s12, real &lat2, real &lon2, real &azi2, real &m12, real &M12, real &M21, real &S12) const

void ArcPosition(real a12, real &lat2, real &lon2, real &azi2, real &s12, real &m12, real &M12, real &M21, real &S12) const

Math::real Distance() const

Namespace for GeographicLib.

GeodSolve is a command-line utility providing access to the functionality of GeodesicExact and GeodesicLineExact (via the -E option).

Definition at line 42 of file GeodesicLineExact.hpp.

◆ BaseClass

◆ mask

Bit masks for what calculations to do. They signify to the GeodesicLineExact::GeodesicLineExact constructor and to GeodesicExact::Line what capabilities should be included in the GeodesicLineExact object. This is merely a duplication of GeodesicExact::mask.

Definition at line 89 of file GeodesicLineExact.hpp.

Constructor for a geodesic line staring at latitude lat1, longitude lon1, and azimuth azi1 (all in degrees).

Parameters

lat1 should be in the range [−90°, 90°].

The GeodesicLineExact::mask values are

• caps |= GeodesicLineExact::LATITUDE for the latitude lat2; this is added automatically;
• caps |= GeodesicLineExact::LONGITUDE for the latitude lon2;
• caps |= GeodesicLineExact::AZIMUTH for the latitude azi2; this is added automatically;
• caps |= GeodesicLineExact::DISTANCE for the distance s12;
• caps |= GeodesicLineExact::REDUCEDLENGTH for the reduced length m12;
• caps |= GeodesicLineExact::GEODESICSCALE for the geodesic scales M12 and M21;
• caps |= GeodesicLineExact::AREA for the area S12;
• caps |= GeodesicLineExact::DISTANCE_IN permits the length of the geodesic to be given in terms of s12; without this capability the length can only be specified in terms of arc length;
• caps |= GeodesicLineExact::ALL for all of the above.

The default value of caps is GeodesicLineExact::ALL.

If the point is at a pole, the azimuth is defined by keeping lon1 fixed, writing lat1 = ±(90° − ε), and taking the limit ε → 0+.

Definition at line 124 of file GeodesicLineExact.cpp.

References GeographicLib::Math::AngNormalize(), GeographicLib::Math::AngRound(), and GeographicLib::Math::sincosd().

◆ GeodesicLineExact() [2/2]

A default constructor. If GeodesicLineExact::Position is called on the resulting object, it returns immediately (without doing any calculations). The object can be set with a call to GeodesicExact::Line. Use Init() to test whether object is still in this uninitialized state.

Definition at line 217 of file GeodesicLineExact.hpp.

◆ Position() [1/6]

Compute the position of point 2 which is a distance s12 (meters) from point 1.

Parameters

Returns

a12 arc length from point 1 to point 2 (degrees).

The values of lon2 and azi2 returned are in the range [−180°, 180°].

The GeodesicLineExact object must have been constructed with caps |= GeodesicLineExact::DISTANCE_IN; otherwise Math::NaN() is returned and no parameters are set. Requesting a value which the GeodesicLineExact object is not capable of computing is not an error; the corresponding argument will not be altered.

The following functions are overloaded versions of GeodesicLineExact::Position which omit some of the output parameters. Note, however, that the arc length is always computed and returned as the function value.

Definition at line 263 of file GeodesicLineExact.hpp.

◆ Position() [2/6]

◆ Position() [3/6]

◆ Position() [4/6]

◆ Position() [5/6]

◆ Position() [6/6]

◆ ArcPosition() [1/7]

Compute the position of point 2 which is an arc length a12 (degrees) from point 1.

Parameters

The values of lon2 and azi2 returned are in the range [−180°, 180°].

Requesting a value which the GeodesicLineExact object is not capable of computing is not an error; the corresponding argument will not be altered.

The following functions are overloaded versions of GeodesicLineExact::ArcPosition which omit some of the output parameters.

Definition at line 371 of file GeodesicLineExact.hpp.

◆ ArcPosition() [2/7]

◆ ArcPosition() [3/7]

◆ ArcPosition() [4/7]

◆ ArcPosition() [5/7]

◆ ArcPosition() [6/7]

◆ ArcPosition() [7/7]

◆ GenPosition()

The general position function. GeodesicLineExact::Position and GeodesicLineExact::ArcPosition are defined in terms of this function.

Parameters

Returns

a12 arc length from point 1 to point 2 (degrees).

The GeodesicLineExact::mask values possible for outmask are

• outmask |= GeodesicLineExact::LATITUDE for the latitude lat2;
• outmask |= GeodesicLineExact::LONGITUDE for the latitude lon2;
• outmask |= GeodesicLineExact::AZIMUTH for the latitude azi2;
• outmask |= GeodesicLineExact::DISTANCE for the distance s12;
• outmask |= GeodesicLineExact::REDUCEDLENGTH for the reduced length m12;
• outmask |= GeodesicLineExact::GEODESICSCALE for the geodesic scales M12 and M21;
• outmask |= GeodesicLineExact::AREA for the area S12;
• outmask |= GeodesicLineExact::ALL for all of the above;
• outmask |= GeodesicLineExact::LONG_UNROLL to unroll lon2 instead of wrapping it into the range [−180°, 180°].

Requesting a value which the GeodesicLineExact object is not capable of computing is not an error; the corresponding argument will not be altered. Note, however, that the arc length is always computed and returned as the function value.

With the GeodesicLineExact::LONG_UNROLL bit set, the quantity lon2 − lon1 indicates how many times and in what sense the geodesic encircles the ellipsoid.

Definition at line 143 of file GeodesicLineExact.cpp.

References GeographicLib::Math::AngNormalize(), AREA, GeographicLib::Math::atan2d(), AZIMUTH, GeographicLib::Math::degree(), GeographicLib::EllipticFunction::Delta(), GeographicLib::EllipticFunction::deltaD(), GeographicLib::EllipticFunction::deltaE(), GeographicLib::EllipticFunction::deltaEinv(), GeographicLib::EllipticFunction::deltaH(), DISTANCE, DISTANCE_IN, GEODESICSCALE, Init(), GeographicLib::DST::integral(), LATITUDE, LONG_UNROLL, LONGITUDE, GeographicLib::Math::NaN(), REDUCEDLENGTH, GeographicLib::Math::sincosd(), and GeographicLib::Math::sq().

Referenced by GeographicLib::GeodesicLine::GenPosition(), SetArc(), and SetDistance().

◆ SetDistance()

◆ SetArc()

◆ GenSetDistance()

Specify position of point 3 in terms of either distance or arc length.

Parameters

Definition at line 288 of file GeodesicLineExact.cpp.

References SetArc(), and SetDistance().

◆ Init()

◆ Latitude()

◆ Longitude()

◆ Azimuth() [1/2]

Returns

azi1 the azimuth (degrees) of the geodesic line at point 1.

Definition at line 579 of file GeodesicLineExact.hpp.

◆ Azimuth() [2/2]

The sine and cosine of azi1.

Parameters

Definition at line 588 of file GeodesicLineExact.hpp.

◆ EquatorialAzimuth() [1/2]

Returns

azi0 the azimuth (degrees) of the geodesic line as it crosses the equator in a northward direction.

The result lies in [−90°, 90°].

Definition at line 597 of file GeodesicLineExact.hpp.

◆ EquatorialAzimuth() [2/2]

The sine and cosine of azi0.

Parameters

Definition at line 606 of file GeodesicLineExact.hpp.

◆ EquatorialArc()

Returns

a1 the arc length (degrees) between the northward equatorial crossing and point 1.

The result lies in [−180°, 180°].

Definition at line 615 of file GeodesicLineExact.hpp.

◆ EquatorialRadius()

Returns

a the equatorial radius of the ellipsoid (meters). This is the value inherited from the GeodesicExact object used in the constructor.

Definition at line 625 of file GeodesicLineExact.hpp.

◆ Flattening()

◆ Capabilities() [1/2]

Returns

caps the computational capabilities that this object was constructed with. LATITUDE and AZIMUTH are always included.

Definition at line 639 of file GeodesicLineExact.hpp.

◆ Capabilities() [2/2]

◆ GenDistance()

The distance or arc length to point 3.

Parameters

Returns

s13 if arcmode is false; a13 if arcmode is true.

Definition at line 659 of file GeodesicLineExact.hpp.

◆ Distance()

◆ Arc()

◆ GeodesicExact

◆ GeodesicLine

The documentation for this class was generated from the following files:

• GeodesicLineExact.hpp
• GeodesicLineExact.cpp